LEVARAGE

Leverage (finance) In finance, leverage (sometimes referred to as gearing in the United Kingdom and Australia) is a general term for any technique to multiply gains and losses.^[1] Common ways to attain leverage are borrowing money, buying fixed assets and using derivatives.^[2] Important examples are:

• A public corporation may leverage its equity by borrowing money. The more it borrows, the less equity capital it needs, so any profits or losses are shared among a smaller base and are proportionately larger as a result.^[3]
• A business entity can leverage its revenue by buying fixed assets. This will increase the proportion of fixed, as opposed to variable, costs, meaning that a change in revenue will result in a larger change in operating income.^[4][5]
• Hedge funds often leverage their assets by using derivatives. A fund might get any gains or losses on $20 million worth of crude oil by posting $1 million of cash as margin.^[6]

Measuring leverage

A good deal of confusion arises in discussions among people who use different definitions of leverage. The term is used differently in investments and corporate finance, and has multiple definitions in each field.^[7]

Investments

Accounting leverage is total assets divided by the total assets minus total liabilities.^[8] Notional leverage is total notional amount of assets plus total notional amount of liabilities divided by equity.^[1] Economic leverage is volatility of equity divided by volatility of an unlevered investment in the same assets. To understand the differences, consider the following positions, all funded with $100 of cash equity:^[9]

• Buy $100 of crude oil with money out of pocket. Assets are $100 ($100 of oil), there are no liabilities, and assets minus liabilities equals owners' equity. Accounting leverage is 1 to 1. The notional amount is $100 ($100 of oil), there are no liabilities, and there is $100 of equity, so notional leverage is 1 to 1. The volatility of the equity is equal to the volatility of oil, since oil is the only asset and you own the same amount as your equity, so economic leverage is 1 to 1.
• Borrow $100 and buy $200 of crude oil. Assets are $200, liabilities are $100 so accounting leverage is 2 to 1. The notional amount is $200 and equity is $100, so notional leverage is 2 to 1. The volatility of the position is twice the volatility of an unlevered position in the same assets, so economic leverage is 2 to 1.
• Buy $100 of crude oil, borrow $100 worth of gasoline, and sell the gasoline for $100. You now have $100 cash, $100 of crude oil, and owe $100 worth of gasoline. Your assets are $200, and liabilities are $100, so accounting leverage is 2 to 1. You have $200 in notional assets plus $100 in notional liabilities, with $100 of equity, so your notional leverage is 3 to 1. The volatility of your position might be half the volatility of an unlevered investment in the same assets, since the price of oil and the price of gasoline are positively correlated, so your economic leverage might be 0.5 to 1.
• Buy $100 of a 10-year fixed-rate treasury bond, and enter into a fixed-for-floating 10-year interest rate swap to convert the payments to floating rate. The derivative is off-balance sheet, so it is ignored for accounting leverage. Accounting leverage is therefore 1 to 1. The notional amount of the swap does count for notional leverage, so notional leverage is 2 to 1. The swap removes most of the economic risk of the treasury bond, so economic leverage is near zero.

Abbrevations

• EBIT means Earnings before interest and taxes.
• DOL is Degree of Operating Leverage
• DFL is Degree of Financial Leverage
• DCL is Degree of Combined Leverage
• ROE is Return on Equity
• ROA is Return on assets

Corporate finance

Accounting leverage has the same definition as in investments.^[10] There are several ways to define operating leverage, the most common.^[11] is:

Financial leverage is usually defined^[8][12] as:

or: